FIVE RISK FACTORS MODEL: PRICING SECTORAL PORTFOLIOS IN THE BRAZILIAN STOCK MARKET

Transcription

1 Revisa Caarinense da Ciência Conábil, ISSN eissn , Florianópolis, SC, Brazil, v. 16, n. 48, p , May/Aug doi: / /rccc.v16n Available a hp://revisa.crcsc.org.br FIVE RISK FACTORS MODEL: PRICING SECTORAL PORTFOLIOS IN THE BRAZILIAN STOCK MARKET MATHEUS DUARTE VALENTE VIEIRA Maser in Business Adminisraion from IAG/PUC-Rio. Tax Audior of he Municipaliy of Cuiabá. Address: Rua Marquês de São Vicene, 225 Gávea Rio de Janeiro/RJ Brazil. vieiramaheus001@gmail.com VINICIUS MOTHÉ MAIA PhD suden a IAG / PUC-Rio. Professor of Accouning a FACC / UFRJ. Address: Av. Paseur room 242 Urca Rio de Janeiro/RJ Brazil. viniciusmohemaia@yahoo.com.br MARCELO CABÚS KLOTZLE Docor of Economics. Professor of he Main Board of IAG/PUC-Rio. Address: Rua Marquês de São Vicene, 225 Gávea Rio de Janeiro/RJ Brazil. klozle@iag.puc-rio.br ANTONIO CARLOS FIGUEIREDO Docor of Economics. Professor of he Main Board of IAG/PUC-Rio. Address: Rua Marquês de São Vicene, 225 Gávea Rio de Janeiro/RJ Brazil. figueiredo@iag.puc-rio.br ABSTRACT The asses risk premium is he cenral variable of he finance models ha seek o esimae he cos of capial of he companies, he cos of his employee, for example, in he evaluaion of he sock price. There are several models used o calculae he risk premium, wih Fama and French models being widely known and widely disseminaed. In 2015, Fama and French inroduced a new model wih he inroducion of wo new risk premiums. Due o he relevance of he heme and he possibiliy of obaining new informaion from his new model, he objecive of his paper is o conduc a sudy in he Brazilian sock marke from a sample composed of companies lised on he São Paulo Sock Exchange (BMF&Bovespa), esing he abiliy of secoral pricing in he risk facors presen in he recen 5-facor model, proposed by Fama and French (2015a). In order o carry ou he research, he companies lised on he Bovespa were used beween January 2008 and December The resuls poin o a greaer imporance of he invesmen risk premium, being saisically significan in hree of he five secors of he economy sudied. Keywords: Pricing Model. 5-Risk Facors. Brazilian Sock Marke. Secor Porfolios. SUR Regression. Submission on 11/22/2016. Review on 02/16/2017. Accep on 22/05/2017.

2 82 FIVE RISK FACTORS MODEL: PRICING SECTORAL PORTFOLIOS IN THE BRAZILIAN STOCK MARKET 1 INTRODUCTION "Wall Sree: money never sleeps". This jargon is no jus a movie name, bu a reflecion of he consan flucuaions in which sock marke prices daily pass. In order o undersand he facors ha give rise o reurns, invesors and academics seek o achieve for decades he key elemens ha drive he sock marke. The echnical and fundamenalis analyzes are he ools used daily by raders, asses managemen, insiuional funds, and agens who are a he forefron of he negoiaions, in an aemp o inerpre he oscillaions and o bea he marke. On he oher hand, academics srive o undersand he facors ha explain he reurn of shares. In his way, we seek o formulae a pricing model, capable of reflecing he key facors ha explain he marke reurn wih he highes possible precision. In he lieraure, afer CAPM, he mos widespread model was he mulifacorial model of Fama and French (1993) ha selecs he risk facors as elemens of he pricing model. Risk facors can be defined as risk exposures refleced in he reurns of a paricular asse class. In his conex, risk facor models have been used no only in he academic field, bu also by quaniaive funds ha ry o capure excess reurns from risk facors presen in he business and macroeconomic environmen. The risk-based invesmen sraegy seeks o idenify drivers of reurns. In he macroeconomic field one, can cie as relevan facors: economic growh, real ineres rae, inflaion, defaul rae, counry risk. Already in he business environmen, liquidiy, marke value, leverage, in addiion o several indices obained from accouning daa. The four-facor model developed by Carhar (1997) succeeded he Fama and French 3- facor model and originaes from he momen sraegy of Jegadeesh and Timan (1993). Such sraegy arises from he finding of he exisence of abnormal reurns posiive for a sraegy based on he selecion of roles, having as parameer he pas performance. The sraegy esablishes a sold posiion for papers wih recen low performance and purchased from hose coming from a recen high rally or accumulaion of earnings in he las 12 monhs. Following his line of sudies, Fama and French (2006) derive from he dividend model, discouning he influence of book o marke (B/M - relaion beween he book value and he marke value) on he capuring of reurns. The main premise of he 5-facor model proposed by Fama and French (2015a) is ha he presen value of a given sock is calculaed from he dividends expeced in fuure financial years, esing he robusness of his model in laer works (Fama & French, 2014, 2015b). The objecive of he sudy is o conduc a sudy in he Brazilian sock marke based on a sample composed of companies lised on he São Paulo Sock Exchange (BMF&Bovespa), esing he abiliy of secoral pricing of risk facors presen in he recen 5-facor model, proposed by Fama and French (2015a). I is imporan o emphasize ha he idea of he presen sudy is no o replicae he original 5-facor model of Fama and French (2015a), bu o use he five risk facors proposed by he auhors in he composiion of a pricing model, hrough a mehodology adaped o he condiions of he Brazilian capial marke. From he selecion of he sample and calculaion of he risk facors, we obained he pricing models o be applied o secoral porfolios assembled year by year. The idea is o show he model's capaciy o price he average weekly reurns of he main secors of aciviy of he companies lised on Bovespa (basic maerials, cyclical consumpion, non-cyclical consumpion, indusrial and public uiliy). 2 LITERATURE REVIEW Markowiz's porfolio selecion heory (1952) was he iniial sep in he developmen of various asse pricing models ha seek o deermine he expeced reurn. The cenral hypohesis is ha invesors make heir decisions backed by wo parameers presen in he probabiliy disribuions of asses: he mean and he variance. These merics refer o he classic risk-reurn relaionship, always inheren o he process of choosing an invesmen. For his reason, Markowiz's framework is also known in he lieraure as a mean-variance model.

3 83 Maheus Duare Valene Vieira, Vinicius Mohé Maia, Marcelo Cabús Klozle and Anonio Carlos Figueiredo Considering he assumpions of his heory, o compose an opimal invesmen porfolio, he economic agen should allocae is resources o he porfolio ha presens he smalles variance among an infinie se of porfolios ha bring a cerain expeced reurn (Caldeira, Moura, & Sanos, 2013). In his conex, he reurn on an invesmen porfolio can be measured by means of he individual expeced reurns of he componen asses, weighed by heir respecive porfolio weighs (Invesmen Science p.166). The variance of he porfolio can be obained from he individual variances of he asses. Diversificaion is a basic principle of his heory. I is considered capable of miigaing non-sysemaic risk (of he companies hemselves), whenever he asses do no have a perfec correlaion wih each oher (oher han ρ = 1). Sysemaic (marke) risk, in urn, canno be eliminaed, bu can be opimized hrough he porfolio of minimum variance, which generaes he lowes risk level for he invesor. In he sock valuaion models, he asse risk premium is he cenral variable in explaining he reurn of hese asses. In his conex, wo lines of research sand ou in he improvemen of he sudy of he CAPM model. One of hese lines of research focused on he dynamic reamen of he model, in which risk facors vary over ime. These models are called condiional CAPM. In hese models, i is no assumed ha he relaionship beween he reurn of he asse and he risk facor is saic. I seeks o reflec he changes ha occur in he marke over ime. The oher line of research sough o sudy muliple risk facors capable of explaining he reurn of he arge asse. The focus was on wha organizaional facors would be able o explain he company's performance. I is in his line ha he presen research fis and seeks o apply he mos recen model of Fama and French, he 5-facor model. In secions 2.1 o 2.3, he evoluion of he uni facor model (CAPM model) o he curren muli-facor model (5-facors) will be explored. 2.1 Capial Asse Pricing Model The porfolio heory was he basis for he works of Sharpe (1964), Linner (1965) and Mossin (1966), who formulaed he CAPM (Capial Asse Pricing Model). The Sharpe-Linner version is he mos widespread in he lieraure, esablishing ha he expeced reurn of he asse ER ( i ) is equal o he sum of he risk-free rae, R f, wih he risk premium of he asse, [ E( R ) R ]. ER ( ) is he expeced reurn on he marke porfolio (sysemaic risk). im m f The CAPM parameer m im is he core of he model and seeks o capure he sensiiviy of he asse o marke porfolio oscillaions. I is calculaed by he quoien beween he acivemarke covariance and he variance of he marke reurn. Therefore, insofar as he sysemaic risk canno be miigaed, invesors would heoreically be compensaed for by higher reurns by carrying higher risk embedded porfolios, in urn capured by he bea sensiiviy of he marke. Anoher well-known version is Black, known as Zero Bea CAPM. The difference in relaion o he previous srand is he subsiuion of he risk-free rae for he reurn of a porfolio Z, wih no correlaion wih he marke porfolio. The resul of he Zero Bea model is ineresing. I srenghens he CAPM insofar as i shows ha he efficien marke porfolio, in erms of mean-variance, can be achieved no only from risk-free loans (CAPM Sharpe-Linner's premise), bu also from he sale o Risk-bearing asses (Fama & French, 2004). CAPM, in is various versions, is buil on he so-called efficien marke hypohesis, encompassing, as premises, he eliminaion of diversifiable risk (hrough he consrucion of a porfolio wih minimal variance), inexisence of ransacion coss, symmeric informaion, raional invesors averse o risk, and marke equilibrium, among ohers. Despie he inabiliy of he premises o reflec he naural condiions of he marke, CAPM served (and sill serves) as a heoreical analyical-base model for he consrucion of more complex models. The CAPM posulaes ha he reurn of an acion can only be explained by he bea parameer. However, since he 1980s, empirical evidences conrary o he explanaory capaciy

4 84 FIVE RISK FACTORS MODEL: PRICING SECTORAL PORTFOLIOS IN THE BRAZILIAN STOCK MARKET of he marke bea appear in he lieraure, such as he work of Sambaugh (1982) and Fama and French (1992). Such sudies show ha he bea-reurn relaionship is less pronounced (or more horizonal) han he prediced by he Sharpe-Linner model. I is imporan o highligh Roll's criique (1977) of he impossibiliy of esing he CAPM model, insofar as he rue marke porfolio, wih all he markeable asses presen in he economy, canno be replicaed. 2.2 The 3-facor model of Fama and French In he search for a pricing model wih greaer scope and abiliy o explain he reurn of papers lised on NYSE, AMEX and NASDAQ, Fama and French (1992) elaboraed a 3-facor model: marke risk, size and B/M raio. The sample consiss of shares of he hree Sock Exchanges beween 1963 and To calculae he model facors, Fama and French (1992) consruced porfolios o replicae he Small Minus Big (SMB) facor, defined by he marke capializaion of he companies, as well as he book marke (High minus Low - HML) facor. The excess marke reurn, m, lr,, presen in he single facor model, will also compose he model: i, lr, i i m, lr, i i i R R R R a b ( R R ) s ( SMB ) h ( HML ) e (1) Wherein Ri, is he reurn of porfolio i in monh ; lr, is he reurn of he asse wih risk free rae in monh ; Rm, is he reurn of he marke porfolio in monh ; SMB is he premium for he size facor in monh ; HML is he premium for he B/M facor in monh ; ei is he error erm of he model. The auhors find evidence of posiive premiums for he hree risk facors; he regression of he model porfolios presens an inercep saisically equal o zero, which validaes he risk facors such as proxies for he pricing model. The model was able o neuralize problems of mulicollineariy beween he facors, besides showing superior explanaory capaciy o he CAPM for he reurns of shares in he American financial marke. Anoher ineresing resul, B/M has explanaory power for he average reurns greaer han he size effec. Dividing he sample ino 12 porfolios, based on B/M, companies wih lower B/M obained an average reurn of 0.3%, while hose wih he highes index reached 1.83% of reurn in he period analyzed. The explanaion for his phenomenon is based on he fac ha shares wih high B/M are considered riskier han hose wih reduced B/M. According o Fama and French (1992), he highes reurn would be a way o compensae for he greaer risk borne by high B/M papers. 2.3 The 5-facor model of Fama and French Fama and French (2006) derive from he dividend model, discouning he influence of B/M on he capure of reurns. The main premise of his model is ha he presen value of a cerain share is calculaed from he dividends expeced in fuure financial years. M is he sum of he dividends discouned by i, he inernal rae of reurn (IRR) of he expeced dividends, supplying he share price in period. By means of an accouning derivaive, hey arrive a he value of he share as: he reurn per share, RPA, less he change in he ne book value per share, B. R M E( RPA B ) (1 i) 1 1 (2) B B B 1 (3)

5 85 Maheus Duare Valene Vieira, Vinicius Mohé Maia, Marcelo Cabús Klozle and Anonio Carlos Figueiredo Dividing he presen value of he dividends (which in heory mus correspond o he marke price of he share, M ) by he value of he ne worh accoun is he inverse of he B/M meric: M B E( RPA 1B1) (1 i) B The derivaion from his cash flow allows he following inferences: ceeris paribus, a lower value of M (higher B/M) implies higher expeced reurn; mainaining fixed B, M and he expeced profi, he increase in he balance shee growh (invesmen, asse expansion) generaes lower expeced reurns. The imporance of his valuaion model is o provide facors ha, included in he pricing model, can efficienly capure he expeced reurns. In his conex, moivaed by he works of Novy-Marx (2012) and Aharoni, Grudy and Zeng (2013), who find favorable evidence for he average reurns and profiabiliy raio, and for he average reurns and invesmen raio, respecively, Fama and French (2015a) added wo new parameers o he original hree-facor model: Ri, Rlr, ai bi ( RM RF ) sismb hi HML rrmw i cicma ei (5) The RMW facor is calculaed from he operaional profiabiliy measured by he company. The financial index ha makes his calculaion possible is he operaing profi/pl raio. Therefore, he facor measures he reurn difference obained by socks wih robus and weak operaing performance. The CMA risk facor is calculaed using he oal asses variaion from year o year as a parameer. The facor idea is o measure he difference in reurn beween companies ha expanded heir oal asses wih more inensiy (more aggressively) and companies ha had more moderae asse expansion, or even had a conracion in heir (conservaive) asse posiion. In a laer sudy, Fama and French (2015b) esed he robusness of his 5-facor model based on anomalies, suggesed by he marke bea lieraure, sock repurchases, volailiy, accruals and iming. The resuls show ha reurns from profiable firms and conservaive invesmen (posiive RMW and CMA) capure high average reurns associaed wih low bea marke, share repurchases and low volailiy. Tesing he 5-facor model in inernaional capial markes, Fama and French (2015c) confirm he exisence of a posiive relaionship of B/M and profiabiliy, and a negaive relaionship of he invesmen, wih he average reurns of he sock markes of Norh America, Europe and Pacific Asia. The model is also esed for he Japanese marke by providing favorable evidence for he explanaory power of he B/M, which does no occur wih profiabiliy and invesmen facors. (4) 3 METHODOLOGY The presen research seeks o invesigae if he adaped 5-facor model is able o accuraely price he variaions of he reurns of secoral porfolios. The mehod used o consruc he porfolios (used o calculae he risk facors) is he 2x2x2x2 model. This mehod produces 8 porfolios, segmened by he median of he merics of he four risk facors (SMB, HLM, RMW, CMA). Some differences from he Fama and French (2015a) mehod should be highlighed. Firsly, he auhors build heir porfolios from monhly value weighed reurns. In his work, equally weighed weekly reurns are used. The merics of he risk facors undergo an adapaion, relaed o he RMW facor, as explained in secion 3.1.

6 86 FIVE RISK FACTORS MODEL: PRICING SECTORAL PORTFOLIOS IN THE BRAZILIAN STOCK MARKET The crieria for inclusion in he sample were hose adoped by Leie, Pino and Klozle (2016), who seek o adap he sample o he condiions of he Brazilian sock marke. The heoreical jusificaions of he adoped mehodology are deailed in secion Sample and Daa Collecion The sample was assembled from socks lised on BMF&Bovespa from January 2008 o December The choice of period is jusified by he large number of iniial public offerings (IPOs) ha occur beween 2006 and In his sense, he collecion of daa from 2008 provides he possibiliy of working wih a wider and more robus sample for he pricing model. Beween February 2006 and June 2008, he domesic sock marke experienced a boom in erms of public lising. During his period, 94 IPOs were auhorized by he Securiies and Exchange Commission, reflecing he favorable macroeconomic scenario ha he Brazilian economy was undergoing. In he sudy, weekly reurn series obained from he closing prices of he companies included in he sample were used. All daa was colleced from he Bloomberg erminal, excep he 30-day SWAP-DI raes, obained from he BMF&Bovespa informaion rerieval sysem. The iniial selecion of he asses o compose he porfolios is carried ou year by year, prospecively, a he end of December of each year. In oher words, he posiion of lised companies wih acive rading a he end of December of each year is used in he iniial gross sampling, which will go hrough he subraced exclusion crieria. The ne sample, obained afer applying he exclusionary crieria, will provide he papers ha will compose he porfolios of he subsequen year. In his conex, he sample is redefined from an annual periodiciy, based on he following crieria: The share mus be raded in a leas 50% of he rading sessions of he year, liquidiy crierion; Excluding shares wih negaive Shareholders' Equiy (PL), companies wih PL<0 characerize insolvency, being able o bias he HML and RMW facors, which direcly use he book value of he PL in is calculaion; Excluding banks and insurance companies, he composiion of he balance shee and he income saemen of he companies of hese segmens have paricular characerisics, requiring a mehodology of own evaluaion for he secors. Is inclusion may bias he model. By applying he aforemenioned crieria, he following amouns of asses were obained year by year: 88 in 2008, 111 in 2009, 197 in 2010, 194 in 2011, 193 in 2012, 175 in 2013, 188 in 2014, and 178 in By obaining he filered asses, hese were segmened ino porfolios, whose selecion crierion was secorial. The calculaion of he risk facors was carried ou from he porfolios assembled. The series of weekly reurns from 2008 o 2015 provided he oal of 417 observaions (weeks) ha, hrough calculaions of weekly risk facors, produced 417 daa for he esimaion of he pricing model. 3.2 Base variables The adjused weekly reurn on shares is used o include dividends. The Bloomberg erminal has a configuraion feaure ha allows embedding mandaory dividends, addiional dividends and ineres on equiy in he reurn of he shares, as well as o adjus hisorical sock prices for splis, inplis, increases and capial reducions. Adjusmens o disribue dividends and corporae evens carried ou by he erminal avoid disorions in weekly reurns, in addiion o embodying he global reurn measured by he shareholder. Applied o he nominal reurn wih dividends is he Neperian logarihm for ransforming he discree reurns ino coninuous ones.

7 87 Maheus Duare Valene Vieira, Vinicius Mohé Maia, Marcelo Cabús Klozle and Anonio Carlos Figueiredo R i, Div P i, i, ln 1 Pi, 7 (6) Wherein P i, is he closing price of he rading day of and Pi, 7 he closing price of he day of he previous week, -7. The quoien of he wo variables provides he weekly variaion of he sock price. We adop he hypohesis of equally weighed weighs o calculae he average weekly reurn of he marke porfolio, measured from he shares ha me he eligibiliy crieria. R n 1 c, Ri, N i 1 (7) Wherein Rc, is he weekly reurn of he porfolio is a week, i, is he sock reurn i in week and N is he number of shares in he porfolio. The choice of adoping equally weighed reurns avoids an inheren problem in he Brazilian sock marke: he high concenraion of rading in a small number of socks. The low dispersion among socks in relaion o he volume raded is a common feaure of capial markes in emerging markes. The B/M index, calculaed on he basis of shareholders' equiy, is aken from he balance shee as of December 31 from -1, and he marke value a he same dae, December 31 from - 1. B M VC PL, dezembro ( 1) (8) VM i, dezembro ( 1) R The marke value of a share (VM ) is a reflecion of he marke's expecaion for he abiliy o generae cash flow and o make profis of a company. The ne equiy ( VC PL, ) is he difference beween he book value of he asses and liabiliies, i is he residual value beween he deb (asses) and he credi (liabiliies) of he balance shee of a company. Unlike he curren sraegy of Jegadeesh and Timan (1993), which uses sock performance in he capial marke o calculae he WML (Winning Minus Losers) risk facor, he RMW (Robus Minus Weakers) facor seeks o reflec he operaional performance of a company, ha is, is abiliy o generae cash flow o he shareholder. In he work of Fama and French (2015a), he meric used is he operaing profi divided by he ne equiy. Operaing income is obained from ne revenue less general and adminisraive sale expenses. Due o he difficuly in accessing he Brazilian daa of hese specific accouns of he income saemen, an adjusmen was made. Operaing profi has been replaced by EBIT. The facor is calculaed from he financial index EBIT/PL. RMW = EBIT VC dez ( 1) PL, dez( 1) (9) This index is similar o ROIC (reurn on invesed capial), a measure ha measures he operaional capaciy of a company o remunerae he capial invesed by he shareholder. The ROIC is calculaed by he EBIAT/Invesed Capial Index. The measure of he denominaor is Earnings Before Ineres Afer Taxes (EBIAT) and he divisor is he invesed capial (or he paidup capial sock), an inegral par of Ne Equiy. This measure reflecs he basic produciviy of he capial invesed in he business (i is he reurn obained by each moneary uni applied in he business). The higher he ROIC, he more aracive i is o inves in he company.

8 88 FIVE RISK FACTORS MODEL: PRICING SECTORAL PORTFOLIOS IN THE BRAZILIAN STOCK MARKET A his poin, i is ineresing o noe ha wo of he risk facors use PL in is composiion (HML and RMW). The use of his balance shee componen as an evaluaion ool has pros and cons. Based on he premise ha accouning informaion carries he fundamenal qualiaive characerisics - relevance and reliable represenaion - i can be considered ha PL is a sable measure, capable of reflecing he generaion of value by he organizaion. On he oher hand, i can be influenced by accouning decisions, regarding he measuremen of asses and liabiliies. As examples, we can cie he procedures adoped o reduce he recoverable value of fixed asses (impairmen ess), and he mehod adoped in he conrol and evaluaion of invenories, among oher decisions capable of affecing he accouning resul and, consequenly, he posiion of he PL ( Damodaran, 2012). Based on a measure of profiabiliy, he RMW facor is deermined by he same fundamenals of he discouned cash flow model: expeced growh, business risk (deerminan of discoun rae) and cash flow generaed (measured resul). In his sense, firms wih higher expeced growh, reduced specific risk and greaer dividend disribuion, ceeris paribus, have higher EBIT/PL. The fourh facor - CMA (Conservaive minus Aggressive), also called INV (invesmen rae) in urn is calculaed based on he change in corporae asses. The calculaion of his risk facor is done by he difference in he posiion of he oal asses beween he end of year -1 and he end of year -2. The idea of he facor is o measure he rae or variaion of invesmen of he companies, refleced in he expansion of asses in he balance shee. CMA A A dez( 1) dez( 2) (10) A dez( 2) There are wo ways for a company o carry ou he aforemenioned expansion: CAPEX (capial expendiure) amoun of capial expendiure ha exceeds depreciaion and he need for capial urnover. The risk facors menioned in his secion can be inerpreed as diversified porfolios, capable of providing differen combinaions of exposure o he merics: marke capializaion (SMB), B/M index (HML), EBIT/PL index (RMW) and changes in asses (CMA). 3.3 Secoral porfolios The secorial porfolios used in his sudy are formed from he companies ha me he inclusion crieria o calculae he risk facors. The secors lised were: basic maerials, cyclical consumpion, non-cyclical consumpion, indusrial and public uiliy, defined from he Bloomberg erminal secor filer, following a similar srucure o he secor indexes prepared by BM&FBovespa: - Basic Maerials Porfolio - covers segmens such as he chemical, pulp and paper, meallurgy, mining and seel indusries. I can be considered he pillar of he producive chain, insofar as i supplies he raw maerials and inpus for he various fields of producive aciviy; - Cyclical Consumpion Porfolio - comprised of wholesale, reail, clohing, exile, auo pars and equipmen, ravel and leisure, hoels and resaurans, real esae developers. This is a secor closely followed by analyss and economiss who work wih economic conjuncure, considered one of he main hermomeers of he level of economic aciviy; - Non-Cyclical Consumpion Porfolio - includes he food and beverage indusry, farming, commerce and disribuion, pharmaceuical, obacco, various services (educaional, laboraorial, highways, operaional leasing). In conras o he volailiy and seasonaliy characerisics of he cyclical consumpion secor, non-cyclical consumpion is characerized by greaer homogeneiy in erms of revenues; - Indusrial Porfolio - composed of companies ha operae in he capial goods indusry (machinery and equipmen), logisics (services and ransporaion maerial) and elecrical equipmen;

9 89 Maheus Duare Valene Vieira, Vinicius Mohé Maia, Marcelo Cabús Klozle and Anonio Carlos Figueiredo - Public Uiliy Porfolio - brings ogeher he subsecors for waer supply, elecriciy, gas and saniaion. They are services rendered by means of delegaion of he public power ha seek o aend o he saisfacion of collecive well-being. Table 1 Spearman correlaion beween Secorial Porfolios Basic Maerial Basic Maerial 1 Cyclical consumpion 0, Non-cyclical Cyclical consumpion Non-cyclical consumpion Indusrial consumpion 0,4255 0, Indusrial 0,7836 0,7260 0, Public Uiliy Public Uiliy 0,4252 0,4464 0,9999 0, Table 1 shows he correlaion beween he weekly reurns of he secor porfolios. The highes correlaions occur beween he indusrial and basic maerials secors (ρ=0.7836) and beween he public uiliy and non-cyclical consumpion secors (ρ = ). All secors presen medium or high correlaion. The presence of lower correlaions by he public uiliy secor wih he reurns of he oher segmens (las line of he able) is jusified because i belongs o a paricular marke srucure, as will be explained in secion 4.2. Is higher correlaion wih he non-cyclical consumpion secor (ρ=0.9999) shows a common characerisic among he secors: he lower dependence of he level of economic aciviy insofar as boh provide essenial services o sociey, characerized by low elasiciy of demand. The secor premiums are calculaed from indusry porfolios assembled on he basis of equally weighed reurns. The juncion of hese parameers gives rise o he following regression model: RCareiraSeorial, Rlr, ai bi ( RM RF ) sismb hi HML rrmw i cicma ei (11) Secion 4 deails he resuls obained from hese regression, esimaed by he OLS (Ordinary Leas Squares) and SUR (Seemingly Unrelaed Regression) mehods. 3.4 Consrucion of porfolios for calculaion of risk facors The base order monh is he end of December of each year, coinciding wih he end of he Brazilian fiscal year. In he firs sage, he shares are ordered according o heir marke value a he end of December of year. This ordering, done in a decreasing sequence, allows he segmenaion of he companies lised in wo porfolios: B (Big) and S (Small). The second order uses he B/M index as a parameer, allowing he formaion of wo new H (High) and L (Low) porfolios. In he hird order, he shares are classified according o he EBIT/PL index, segmening he porfolios in R (Robus) and W (Weak). Finally, in he fourh order, he meric becomes he oal change in asses, or he invesmen rae, leading o he unfolding of he porfolios in C (Conservaive) and A (Aggressive). This procedure is repeaed eigh imes a he end of each year of he sudy period (2008 o 2015). In all four orders, he parameer used o separae porfolios is he median of he base variables (marke value, B/M, EBIT/PL, change in oal asses). The median herefore serves as a dividing line for porfolio segmenaion. This way of building he porfolios produced eigh ses of diversified asses (porfolios) ha allowed, each year, he calculaion of risk facors, described in he following secion. 3.5 Calculaion of Risk Facors The main pricing sudies wih risk facors, such as Fama and French (1993), use monhly reurns o calculae hem. On he oher hand, hey analyze an exended period of ime. In he case of his sudy from 1963 o 1991.

10 90 FIVE RISK FACTORS MODEL: PRICING SECTORAL PORTFOLIOS IN THE BRAZILIAN STOCK MARKET In he presen sudy, given he shorer exension of he invesigaed period, we oped o work wih weekly reurns, in order o increase he number of observaions and, hus, o measure more accuraely he calculaion of he risk facors. The marke facor is calculaed from he difference beween he weekly evenly weighed reurns and he weekly risk free rae, R, compued from linear inerpolaion performed from he lr 30-day SWAP-DI rae. The difference beween he wo merics provides he excess reurn R c, of he porfolio c a day :: n 1 c, i, lr N i 1 R R R (12) Calculaed weekly, from a long posiion in he porfolio wih shares of companies wih low marke capializaion (Small) and sold in shares of companies of grea marke value (Big). The difference in he weekly reurn beween he porfolios provides he SMB risk facor. Calculaed weekly, from a long posiion in he porfolio wih shares of companies wih a high B/M raio and sold in shares of companies wih a low raio. The difference in reurn beween he wo posiions provides he HML risk facor. Calculaed weekly, from a posiion bough in he porfolio wih socks of companies ha obained robus operaing performance (Robus) and sold in shares of companies wih weak operaing performance (Weak). These performance measures were compued based on he operaing profi/pl obained a he end of each year -1. The difference in reurn beween he wo posiions provides he RMW risk facor. Calculaed weekly, from a long posiion in he porfolio wih shares of companies ha had reduced invesmen raes beween he financial years (Conservaive) and sold in shares of companies ha expanded heir asses wih greaer inensiy (Aggressive). The difference in reurn beween he wo posiions provides he CMA risk facor. Table 2 shows he presence of a low correlaion beween he risk facors, a posiive aribue for he pricing model, insofar as i reduces possible muicolourariy problems among he model variables. Table 2 Spearman correlaion beween Secorial Porfolios Rm-Rf SMB HML RMW CMA Rm-Rf 1 SMB -0, HML 0,2097-0, RMW -0,2423-0,0402-0, CMA -0,0884 0,0447 0,0029 0, We highligh he inverse correlaion beween he marke premium and he SMB facor (ρ= ) and he RMW facor (ρ= ), he mos inense of he correlaion marix. 4 RESULTS This secion presens he search resuls. The mehods are applied o he reurns of he five proposed secoral porfolios, each one based on he five calculaed risk facors. From he secor porfolio premiums used as explained variable and risk facors as explanaory variables, five linear regression are formed, which seek o explain he relaionship beween secor porfolio reurns and risk facors. The SUR mehodology is processed in wo sages. In he firs sep, OLS regression residuals are used o esimae he covariance marix of he errors of he equaions. In a second momen, he coefficiens of he regression were esimaed via GLS, when he previously esimaed covariances were applied (Duare, Lamounier, & Takamasu, 2007).

11 91 Maheus Duare Valene Vieira, Vinicius Mohé Maia, Marcelo Cabús Klozle and Anonio Carlos Figueiredo If he error covariance marix obained in he firs sep is zero, he OLS and SUR mehods are equivalen. As a non-zero covariance marix, he SUR mehod performs he correcion of residues, generaing greaer accuracy in he esimaion process (Neves, 1996). The resuls obained by he sudy corroborae he presence of a non-zero covariance 2 marix for he pricing model, refleced in he superioriy of he R adjused from regression esimaed by he SUR mehod in comparison o hose esimaed by OLS, as demonsraed in secion 4.2. The opion by he SUR mehod follows he Cosa and Neves (2000) approach, which, applied o he 5-facor model, makes i possible o es he saisical significance of he four risk facors ha expand he CAPM model a he same ime, as i reflecs he capaciy of he Adjusmens in he marke premium of secor porfolios. 4.1 Saisical Analysis Iniially, a preliminary analysis of he daa was made from he correlaion marix and graphical visualizaion of he series of risk facors. The firs sep was o undersand in a preliminary way he inerrelaionship of variables. In a second momen, he OLS and SUR mehods were evaluaed (secion 4.2). Table 3 Saionary Tesing Reurns Augmened p-value Dickey-Fuller Rm-Rf -5,3744 <0,01 SMB -4,9524 <0,01 HML -6,7011 <0,01 RMW -6,8917 <0,01 CMA -6,0431 <0,01 The Augmened Dickey-Fuller (ADF) es is performed for he five risk facors of he model in order o verify wheher he reurns are saionary or no. The imporance of he es is due o he fac ha non-saionary series have a emporal endency; hey may presen high explanaory power even if he variables are no correlaed (Brooks, 2014). The resuls of he saionariy ess are shown in Table 3 for he reurns of he risk facors and in Table 6 for hose of he secor porfolios. No esed reurn series presened uni roo. They are saionary. Figure 1. Series of weekly reurns of risk facors: Jan-2008 o Dec-2015 Source: Prepared by he auhors. Analyzing he graphs of he behavior of he risk facors, one can observe cerain behaviors for he period of analysis. The firs of hese is he srong acceleraion of spreads

12 92 FIVE RISK FACTORS MODEL: PRICING SECTORAL PORTFOLIOS IN THE BRAZILIAN STOCK MARKET volailiy caused by he subprime crisis, from he fourh quarer of 2008, remaining unil he middle of During his period, here is a paricular behavior on he par of he CMA facor, when he invesors direc heir resources o conservaive companies, o he derimen of he bold ones. This movemen ha reflecs a process of risk aversion is ranslaed ino he posiive spread of he CMA facor. Anoher ineresing scenario, a new acceleraion of spreads (less inense han ha occurred a he end of 2008) occurs from he end of 2010, noably in he marke premium (Rm- Rf) and in he CMA facor, his ime drawn by he European deb crisis, promoed by srong budge deficis linked o he rise in public deb in European counries. The facor, however, ha effecively riggered he new cycle of volailiy was he onse of global marke fears wih he possibiliy of defaul on Greek deb from he second half of This fear was confirmed years laer, more precisely on June , wih he expiraion of he deadline and non-paymen of he axiing of he deb conraced wih he IMF (Inernaional Moneary Fund). The hird and final widening of he spreads of he series occurs from he las quarer of 2014, saring from he presidenial elecions in Brazil. The increase in variaion is clearly seen in he HML and RMW facors, persising during he year 2015, as a resul of Presiden Dilma's coninued presence in power, linked o he macroeconomic scenario of sagflaion in he Brazilian economy. Table 4 Descripive Saisics of Risk Facors Saisic Rm-Rf SMB HML RMW CMA Maximum 0,1700 0,1010 0,0763 0,0357 0,1046 Minimum -0,3422-0,1206-0,0565-0,0665-0,0499 Average -0,0086-0,0025-0,0009 0,0019 0,00004 Medium -0,0029-0,0016-0,0005 0,0028-0,0009 Sandard deviaion 0,0489 0,0183 0,0058 0,0135 0,0145 Asymmery -3,72-0,49 0,29-0,69 1,15 Kurosis 24,12 9,78 6,94 5,59 10,40 Jarque-Bera <0,01-5,69 <0,01-7,32 <0,01-6,44 <0,01 7,10 <0,01 362,5 Descripive saisics of risk facors (Table 4) show he presence of righ asymmery for he Rm-Rf, SMB and RMW facors, and lef asymmery for he CMA. The HML facor, on he oher hand, presens more symmerical reurns. Asymmery o he righ of he marke premium is expeced, given he combinaion of low performance of he Brazilian sock exchange, ied o high ineres raes; for he RMW facor, he opposie was expeced. In relaion o he CMA, wha is expeced is ha he low profiabiliy of he capial marke in a macroeconomic conex ha is unfavorable o leveraged companies generaes a superior performance on he par of he conservaive organizaions. The marke facor is he mos volaile (σ=0.0489), he oher facors have lower volailiies, all below 2%. The coefficien of variaion (CV) was also presened, embodied in he raio beween sandard deviaion and he average, as a way of measuring volailiy. The Jarque- Bera es rejecs he null hypohesis of normaliy for he risk facors. The ADF es is also performed for he variables explained. The secoral porfolio premiums do no have a uni roo, as shown in Table 5. The analysis of uni roo exisence is imporan o verify he possibiliy of modeling hrough regression. The exisence of a uni roo would make his mehodology impossible.

13 93 Maheus Duare Valene Vieira, Vinicius Mohé Maia, Marcelo Cabús Klozle and Anonio Carlos Figueiredo Table 5 Saionary Tesing Reurns Augmened Dickey-Fuller p-value Basic Ma. -6,1297 <0,01 Cyclic Cons. -5,2204 <0,01 Non-Cyclic Cons. -5,7654 <0,01 Indusrial -5,7271 <0,01 Public Uiliy -6,3722 <0,01 Figure 2 shows he reurn series of secoral premiums. Ineresingly, he behavior of he cyclical consumer secor premiums during he second shock (2011) is more inense han ha of he oher secors. This phenomenon can be explained by he wihdrawal of he counercyclical fiscal simulus graned afer he 2008 crisis coupled wih a conracionary moneary policy in an aemp o conain he acceleraion of he inflaion rae and appreciaion of he real afer a year of robus economic growh (in 2010 he Brazilian GDP grew 7.5%). Figure 2. Weekly reurns series of secor porfolios: Jan-2008 o Dec-2015 Source: prepared by he auhors. Figure 2 also reflecs he volailiy of secor premiums brough by he presidenial race. China's macroeconomic deceleraion scenario, domesic inflaionary pressures, rising ineres raes, srong depreciaion of he real coupled wih he beginning of a fiscal adjusmen process by he governmen affeced he purchasing power of Brazilians and, consequenly, he level of consumpion. The secors of cyclical consumpion and basic maerials clearly refleced he effecs of his adverse scenario. Table 6 Descripive Saisics of Secoral Porfolio Premiums Saisic Mb Cc Cnc Ind UP Maximum 0,2816 0,1381 0,2582 0,1927 0,1791 Minimum -0,3903-0,2061-0,2235-0,2971-0,1832 Average -0,0034-0,0023-0,0016-0,0032-0,0009 Medium -0,0027-0,0007-0,0002-0,0007 0,0005 Sandard deviaion 0,0487 0,0358 0,0329 0,0348 0,0304 Asymmery -1,48-1,08-0,39-1,61-0,45 Kurosis 18,68 9,57 19,60 19,28 9,55 Jarque-Bera <0,01-14,32 <0,01-15,56 <0,01-20,56 <0,01-10,87 <0,01-33,78 The descripive saisics of secor porfolios (Table 6) demonsraes he presence of higher volailiy of weekly reurns by he porfolio of commercial maerials (σ=0.0487) followed by cyclical (σ=0.0358) and indusrial (σ=0.0348) consumpion, which makes sense insofar as hey are more sensiive o flucuaions in he level of economic aciviy (secors wih higher price

14 94 FIVE RISK FACTORS MODEL: PRICING SECTORAL PORTFOLIOS IN THE BRAZILIAN STOCK MARKET elasiciies and demand income). We also highligh he righ asymmery of reurns of all secors (common characerisic in he sock marke), more accenuaed in non-cyclical consumpion and public uiliy. The Jarque-Bera es rejecs he null hypohesis of normaliy of he weekly premiums for all secor porfolios. 4.2 Regression In his secion, he parameers obained from regression esimaed by he SUR mehod will be presened. The economic package used for he esimaion process was R Sudio. For correlaion of he regression esimaes, he Newey-Wes covariance marix (HAC marix) was applied. The resuls obained by he OLS mehod were no presened o save space and no o inerfere wih he reader (and can be sen o ineresed paries). The comparison beween he resuls of he wo mehods of esimaion demonsraed he reducion of he sandard errors 2 obained by he SUR mehod, also refleced in he R empirically adjused superior o ha obained by means of he OLS mehod. The reurn of he firs secoral porfolio, of commercial maerials (Table 7), poins o he marke price and RMW as saisically significan facors a he 1% significance level. I is ineresing o noe he relevance of profiabiliy (RMW) in he porfolio price of commercial maerials, a volaile secor in erms of resuls (a negaive variaion of 1% in he RMW causes a posiive oscillaion of 0.44% in he reurn of he porfolio of commercial maerials). Is aciviy is basically concenraed in he circulaion of commodiies, wih low value added, dependen on he inernaional prices of hese raw maerials and inpus, a facor ha impacs he profiabiliy of hese organizaions. Hedge operaions in fuure markes are usually carried ou by he reasuries of hese companies, an aemp o miigae his volailiy. The significan 5% inercep provides a cavea for he applicaion of he model in his secor. Table 7 Basic Maerials SUR Regression RMB, R, a b ( R R ) s SMB h HML rrmw c CMA e lr i i M F i i i i i Variables Coefficien Sandard-Error Saisic p-value Inercep 0, , ,57 0,0104** Rm-Rf 1, , ,82 0,0000*** SMB -0, , ,68 0,4938 HML 0, , ,74 0,4567 RMW -0, , ,87 0,0043*** CMA 0, , ,27 0, Noe: R adjused = Significance: ***, ** and * correspond o 0.01, 0.05 e 0.1, respecively. In he second secoral porfolio, he cyclical consumpion (Table 8), he saisically significan facors were marke premium, RMW and CMA. I should be noed ha for his porfolio, as well as for non-cyclical consumpion, he inercep was saisically significan a 1%, 2 wih a cavea for he model applied in hese secors, which is conrased by he high R adjused from he respecive models, 86.29% and 87.94%, respecively.

15 95 Maheus Duare Valene Vieira, Vinicius Mohé Maia, Marcelo Cabús Klozle and Anonio Carlos Figueiredo Table 8 Cyclic Consumpion SUR Regression RCC, R, a b ( R R ) s SMB h HML rrmw c CMA e lr i i M F i i i i i Variables Coefficien Sandard-Error Saisic p-value Inercep 0, , ,40 0,0007*** Rm-Rf 1, , ,44 0,0000*** SMB 0, , ,64 0,1026 HML 0, , ,15 0,2514 RMW 0, , ,18 0,0298** CMA -0, , ,32 0,0207** 2 Noe: R adjused = Significance: ***, ** and * correspond o 0,01, 0,05 e 0,1, respecively. In he hird secoral porfolio, of non-cyclical consumpion (Table 9), he significan facors were marke premium, SMB and HML. The SMB and HML coefficiens show ha a small negaive variaion in he reurns of hese facors (-0.12% and -0.18%) causes a posiive change in he non-cyclical consumpion porfolio (+ 1%). Table 9 Non-Cyclic Consumpion SUR Regression RCNC, R, a b ( R R ) s SMB h HML rrmw c CMA e lr i i M F i i i i i Variables Coefficien Sandard- Saisic p-value Error Inercep 0, , ,17 0,0000*** Rm-Rf 0, , ,18 0,0000*** SMB -0, , ,00 0,0466** HML -0, , ,44 0,0006*** RMW 0, , ,04 0,2957 CMA 0, , ,27 0, Noe: R adjused = Significance: ***, ** and * correspond o 0,01, 0,05 e 0,1, respecively. In he fourh secorial porfolio, he indusrial one (Table 10), he relevan facors were marke premium and CMA. The significan CMA facor poins ou a posiive influence of he invesmen rae on he reurns of he indusrial secor (a variaion of 0.24% in he CMA causes a 1% oscillaion in he reurn of he indusrial porfolio). This relaionship makes sense insofar as he secor is formed by companies wih a high asse posiion, capial inensive, whose main aciviy is he circulaion of capial goods, jusifying he inense sensiiviy of he premiums of he indusrial porfolio in relaion o he variaion of asses (CMA). Table 10 Indusrial SUR Regression RIND, R, a b ( R R ) s SMB h HML rrmw c CMA e lr i i M F i i i i i Variables Coefficien Sandard-Error Saisic p-value Inercep 0, , ,19 0,0287** Rm-Rf 1, , ,80 0,0000*** SMB 0, , ,90 0,3685 HML -0, , ,59 0,5558 RMW 0, , ,08 0,2797 CMA 0, , ,26 0,0242** 2 Noe: R adjused = Significance: ***, ** and * correspond o 0,01, 0,05 e 0,1, respecively. In he fifh secoral porfolio, of public uiliy (Table 11), he significan facors were marke premium, SMB and CMA. The SMB facor, significan a 1%, has an inverse raio of 0.42% wih he reurn of he public uiliy porfolio. This behavior has an inuiive explanaion, which sems from he marke srucure of he public uiliy secor based on he presence of

16 96 FIVE RISK FACTORS MODEL: PRICING SECTORAL PORTFOLIOS IN THE BRAZILIAN STOCK MARKET barriers o enry due o legal regulaion (inheren in he concession process for he exploiaion of public uiliy services) and he producion process of economies of scale), making i close o a monopoly srucure. This feaure reflecs he influence of he size facor (SMB) on he uiliies secor pricing. Table 11 Public Uiliy SUR Regression RUP, R, a b ( R R ) s SMB h HML rrmw c CMA e lr i i M F i i i i i Variables Coefficien Sandard-Error Saisic p-value Inercep 0, ,0008 1,57 0,0922* Rm-Rf 0, , ,63 0,0000*** SMB -0, ,0482-7,03 0,0000*** HML 0, ,0658 1,37 0,1720 RMW 0, ,0665 1,43 0,1531 CMA 0, ,0620 2,57 0,0106** 2 Noe: R adjused = Significance: ***, ** and * correspond o 0,01, 0,05 e 0,1, respecively. The marke premium is saisically relevan in all esimaed regression, which corroboraes is conribuion o he explanaory capaciy of he 5-facor model, srenghening he marke bea as he mos relevan componen of he pricing model. 5 CONCLUSIONS The presen work used he componens of he 5-facor risk model proposed by Fama and French (2015a) o verify heir respecive influences on Brazilian sock marke reurns. The invesigaed asse class was he weekly reurns of secor porfolios. In order o obain he componens of he pricing model, he 2x2x2x2 porfolio mehod was used, which produced eigh porfolios, based on he variables inheren o he risk facors (marke value, B/M, EBIT/PL and asse variaion). The ordering was carried ou in four seps, producing a each sep wo porfolios, obained by a cuing mehodology ha uses he median of he four facors menioned above. Having he weekly reurns equally weighed from hese porfolios, he risk facors are obained by means of a simple difference of averages. In he las sep, he model was esed. The chosen esimaion process was he muliple linear regression of he SUR ype. The resuls poin ou he imporance of he saisically significan marke premium for all five secors esed. In addiion o he expeced significance of his premium, he risk premium ied o invesmens was significan in hree of he five secors of he economy sudied. This shows he abiliy o explain he amoun of invesmen in relaion o he reurn of he companies. This fac in paricular shows managers how imporan i is o reflec on he organizaion's invesmen policy due o is impac on resuls. I is ineresing o noe in he resuls ha an increase in invesmens does no always have a posiive impac on he performance of he company a ha ime, a fac verified in he negaive coefficien of he cyclical consumpion secor, unlike he Indusrial and Public Uiliy secors, which had posiive coefficiens. The presence of significan inerceps, a a significance level of 1% for he consumpion secors (cyclical and non-cyclical) and 5% for hose of basic and indusrial maerials, and of 10% for public uiliy shows he exisence of influences in he reurns of secor porfolio premiums no capured by he 5-facor model. I conrass wih his resul, as favorable poins o he pricing model, he low correlaion beween he risk facors (avoiding possible problems of muicollecariy) and he high 2 explanaory power of he facor model refleced in he R adjused from he respecive regression. One of he limiaions of he sudy is he size of he Brazilian sock marke, which makes i difficul o consruc diversified porfolios for periods prior o 2008, before he IPO boom

17 97 Maheus Duare Valene Vieira, Vinicius Mohé Maia, Marcelo Cabús Klozle and Anonio Carlos Figueiredo menioned in secion 3.1. The number of lised companies and he low volume of rading in he sock marke are also refleced in he difficuly of implemening oher mehodologies for porfolio consrucion. In heir sudy, Fama and French (2015a) se up 2x4x4 (32 porfolios), 5x5 (25 porfolios) porfolios, segmening porfolios from quariles and quiniles o conrol variables, for example, difficul replicaion echniques for he Brazilian marke. Therefore, he relevance of adaping he pricing models o he condiions of he capial marke invesigaed is emphasized. The esimaion process is also a limiaion. I is recommended ha fuure research uses daa in panels, based on he use of ime series conjugaed wih cross-secion. The use of he GRS saisical es, adoped in he sudy by Fama and French (2015a), may be an economeric echnique used o validae pricing models ha adop panel daa as he esimaion mehod. REFERENCES Aharony, G., Grudy, B. & Zeng, Q. (2013). Sock reurns and he Miller Modigliani valuaion formula: revisiing he Fama French analysis. Journal of Financial Economics, 110(2), Black, F, Jensen, C., & Scholes, M. (1972). The capial asse pricing model: some empirical ess. Sudies in he Theory of Capial Markes, Praeger Publishers Inc, 54 p. Brooks, C. (2014). Inroducory Economerics for Finance (3rd. ed.). Cambridge Universiy Press: New York, 740 p. Caldeira, J, Moura, G., & Sanos, A (2013). Seleção de Careiras Uilizando o Modelo. Revisa Brasileira de Economia, 67(1), Carhar, M.M. (1997). On persisence in muual fund performance. Journal of Finance, 52(1), Cosa, N. da, Jr., & Neves, M. (2000). Variáveis fundamenalisas e os reornos das ações. Revisa Brasileira de Economia, 54(1), Damodaran, A. (2012). Invesmen Valuaion: Tools and Techniques for Deermining he Value of Any Asse (3rd. ed.) Wiley Finance, 992 p.. Duare, P., Lamounier, W., & Takamasu, R. (2007). Modelos Economéricos para Dados em Painel: Aspecos Teóricos e Exemplos de Aplicação à Pesquisa em Conabilidade e Finanças. Anais do Congresso USP de Conroladoria e Conabilidade, São Paulo, SP, 7. Fama, E., & French, K. (1992). The cross-secion of expeced sock reurns. Journal of Finance, 47(2), Fama, E., & French, K. (1993). Common risk facors in he reurns on socks and bonds. Journal of Financial Economics, 33(1), Fama, E., & French, K. (1995). Size and book-o-marke facors in earnings and reurns. Journal of Financial Economics, 50 (1), Fama, E., & French, K. (2004). The Capial Asse Pricing Model: Theory and Evidence. Journal of Economic Perspecives, 18(3), Fama, E., & French, K. (2006). The Value Premium and he CAPM. Journal of Finance, 61(5), Fama, E., & French, K. (2015a). A five-facor asse pricing model. Journal of Financial Economics, 116, Fama, E., & French, K. (2015b). Dissecing Anomalies wih a Five-Facor Model. Fama-Miller Working Paper, Tuck School of Business Working Paper No Fama, E., & French, K. (2015c). Inernaional Tess of a Five-Facor Asse Pricing Model. Fama- Miller Working Paper, Tuck School of Business Working Paper No Jegadeesh, N., & Timan, S. (1993). Reurns o buying winners and selling loosers: Implicaions